686 



SCIENCE. 



[N. S. Vol. VII. No. 177. 



certain amount of intergrading between 

 species. What is needed is a method of 

 precisely defining the degree of isolation 

 and the degree of divergence necessary for 

 distinct species. 



II. Method of attaining a Precise Criterion 

 of Species. We shall accept in what follows 

 the general opinion that the distinction be- 

 tween species and varieties is on6 of degree 

 of divergence and degree of segregation. 

 The question is always where to draw the 

 line. 



In drawing the line between species and 

 varieties we must act somewhat arbitrarily, 

 just because there is no natural division 

 between species and varieties — one shades 

 over into the other. We must, however, 

 have regard to usage— recent usage, on 

 the whole — ^because species have never be- 

 fore been studied so critically and so exten- 

 sively as to-day. We must seek to define 

 the position of the liae with precision, i. e. , 

 quantitatively. 



1. The General Method. Any adequate 

 quantitative method of study ing species must 

 start with the individual. It must recognize 

 that a species is composed of individuals, 

 each differing more or less in any quality 

 from every other individual of the species. 

 The species exist not because all of its com- 

 ponent individuals are alike in all respects, 

 but because in certain qualities, such as size, 

 color or form, they tend to group themselves 

 about a certain typical condition, which is 

 at the same time the most frequent condit- 

 ion. We may call it the mode.* 



Normally, this tendency for measure- 

 ments of qualities to group themselves about 

 the mode follows a very definite law. This 

 law is the same as that followed by the 

 deviations of a large number of rifle bullets 

 from the center of the target at which they 

 were aimed. It is known as the Law of 



* As Professor Minot has suggested to me, ' center 

 of Tariation ' would be a more suggestive term. Mode 

 has the convenience of brevity. 



Error, and is described in text-books on 

 Least Squares. According to this law the 

 smallest errors are the commonest : the 

 larger ones are rarer, and the errors on one 

 side of the mode are counterbalanced by an 

 equal number of errors of the same size on 

 the other side of the mode. If we lay off at 

 equal intervals on a horizontal line a series 

 of points corresponding to the successive 

 classes of magnitude of an organ, and erect 

 at each one of these points vertical lines 

 proportional in length to the number of cases 

 falling in that class, the curve made bj' join- 

 ing their tops will be a normal variability 

 curve (Fig. 1) . This curve is a definite one 

 capable of being expressed by a mathemat- 

 ical formula* and of being subjected to 

 further analysis. 



The curve will, however, vary in certain 

 respects with each species measured. Espe- 

 cially will the curve vary in steepness. In 

 some cases 50 per cent, or even more of the 

 individuals will occur in the middle class — 

 at the mode. In other cases 10 per cent, or 

 even less will lie here. In the former case 

 the curve will be very steep — the horizontal 

 distance between the two ends of the curve, 

 the range, will be small — the character is 

 somewhat invariable or conservative. In 

 the latter case the range of variation will 

 be very great — the character is, we may say, 



* The formula is 3/ = i-.« K^x^^ ju ^hich k and h 

 are constant for any curve. 



